The Seiberg-Witten invariants of negative definite plumbed 3-manifolds

Details The Seiberg-Witten invariants of negative definite plumbed 3-manifolds The Seiberg-Witten invariants of negative definite plumbed 3-manifolds

2010-03-05

arxiv.org/abs/1003.1254v2

Mathematics

Algebraic Geometry

This second version contains some additional connections with the lattice cohomology associated with the plumbing graph

Scientific paper

We consider a connected negative definite plumbing graph, and we assume that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg-Witten invariant of this manifold. The first one is the constant term of a `multivariable Hilbert polynomial', it reflects in a conceptual way the structure of the graph, and emphasizes the subtle parallelism between these topological invariants and the analytic invariants of normal surface singularities. The second formula realizes the Seiberg-Witten invariant as the normalized Euler characteristic of the lattice cohomology associated with the graph, supporting the conjectural connections between the Seiberg-Witten Floer homology, or the Heegaard-Floer homology, and the lattice cohomology.

Affiliated with

Also associated with

No associations

Rating

The Seiberg-Witten invariants of negative definite plumbed 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Seiberg-Witten invariants of negative definite plumbed 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Seiberg-Witten invariants of negative definite plumbed 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687655